Question

For this item select in the choice matrix by clicking the appropriate boxes in each row

Answer 1

Answer:

$(a):\ y = \frac{x + 3}{7}$ --- Function

$(b):$ Not a function

$(c):$ A function

Step-by-step explanation:

Given

See attachment

Required

Determine if each relation is a relation or not

A function is represented as: $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)...(x_n,y_n)\}$

Where

$x = domain$ and $y = range$

For a relation to be a function:

No x value (in other words, the domain) must be repeated

$(a):\ y = \frac{x + 3}{7}$

The above relation is a function. This is so because every unique value of x have a unique value of y.

In other words:

No two domains exist for a range

Conclusively, it is a one-to-one function

$(b):$

$\begin{array}{ccccc}x & {-2} & {-2} & {1} & {3} \ \\ y & {-5} & {-1} & {3} & {7} \ \ \end{array}$

In the above table, we have:

$(x_1,y_1) = (-2,5)$ and $(x_2,y_2) = (-2,-1)$

The domain (-2) points to range (5 and -1).

Based on the condition that no two domain should point to the same range, we can conclude that this is not a function.

$(c):$

$\begin{array}{ccccc}x & {-3} & {-1} & {1} & {3} \ \\ y & {-4} & {-4} & {2} & {2} \ \ \end{array}$

In the above table, we have the domain to be:

$x = \{-3,-1,1,3\}$

We can see that no x value is repeated.

Hence, this is a function.